A circular dividing engine graduates arcs of navigational and other mathematical instruments. Prior to its invention, the scales on such instruments were marked out by skilled craftsmen in a process called "dividing." This method could be quite accurate, but it was extremely tedious and only a few experts were qualified to do it, which meant that accurate instruments took a long time to make and were quite expensive. In addition, the value of the instrument depended entirely upon the accuracy of the maker and his tools.

The incentive to develop a dividing engine came from a major navigational problem: how to find a ship's longitude. In the eighteenth century Britain depended on its navy for defense and its merchant ships for trade, so accurate navigation was essential. The British government set up the Board of Longitude in 1714, which offered a top prize of £20,000 for a way of finding longitude to within thirty nautical miles, and there were smaller awards for related innovations.

In the 1760's, John Harrison and Tobias Mayer developed practical methods of finding longitude at sea; the former by building an accurate chronometer, and the latter by tabulating the motion of the Moon. Both methods required accurate angle-measuring instruments, such as the octant and sextant, to measure the altitudes of heavenly bodies, and spurred a demand for these instruments, but accurately dividing such small scales by hand slowed production.

English instrument maker Jesse Ramsden provided the solution by mechanizing dividing. Ramsden's first dividing engine was completed about 1766, but was not accurate enough for navigational and astronomical instruments. His second engine, completed about 1775, was a complete success, however. The Board of Longitude awarded Ramsden £300, on condition that he disclose the engine's secrets. It then bought the engine for £315 while allowing Ramsden to retain and use it, providing he train up to ten other instrument makers how to duplicate and use the engine. He also had to publish a description of the engine, with enough detail to allow other instrument makers to duplicate it.

The dividing engine was simple to operate. The instrument being divided was fixed to a large wheel on top of the engine. When the treadle was pressed, the wheel and the instrument were turned through a fixed angle. Then with the right hand, a cutting tool guided by a system of swinging links was used to mark the instrument scale. The process was completed until the complete scale had been divided. Although this was many times faster than hand-dividing, it was backbreaking work having to lean over the engine to work on a small instrument.

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"Dividing Engine." Smithsonian National Museum of American History. americanhistory.si.edu/collections/navigation/object.cfm?recordnumber=694508
Leiserowitz, Anthony A. "The Dividing Engine in History." The Museum of Surveying. www.surveyhistory.org/the_dividing_engine1.htm

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